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GB.GetNthSyz
Syntax
GB.GetNthSyz(M:IDEAL or MODULE,N:INT):MODULE
Summary
returns the part of the Nth syzygy module computed so far
Description
This function, if used after executing Res(M)
, returns the Nth
syzygy module for M. Within the Interactive Groebner Framework, in
which resolutions may be computed one step at a time, the function
returns the part of the Nth syzygy module computed so far. In
contrast, the function Syz
always determines the complete syzygy
module even from within the Interactive Groebner Framework.
example
Use R ::= Q[t,x,y,z];
I := Ideal(x^2-yt,xy-zt,xy);
GB.Start_Res(I);
GB.Step(I);
GB.GetNthSyz(I,1); GB.GetNthSyz(I,2);
Module([0])
-------------------------------
Module([0])
-------------------------------
GB.Step(I);
GB.GetNthSyz(I,1); GB.GetNthSyz(I,2);
Module([0, 0])
-------------------------------
Module([0])
-------------------------------
GB.Steps(I,5);
GB.GetNthSyz(I,1); GB.GetNthSyz(I,2);
Module([-xz, -y^2, yz])
-------------------------------
Module([0])
-------------------------------
GB.Complete(I);
GB.GetNthSyz(I,1); GB.GetNthSyz(I,2);
Module([-xz, -y^2, yz], [tz, xy, 0], [0, -x^2 + ty, -tz], [-x^2 + ty, 0, xy])
-------------------------------
Module([-x, -y, 0, z], [-t, -x, -y, 0])
-------------------------------
See Also